DOI: 10.5817/FAI2018-1-1 No. 1/2018
5
Causality in the Polish Housing Market:
Evidence from Biggest Cities
Krzysztof Drachal
University of Warsaw
Faculty of Economic Sciences
Warsaw, Poland
Abstract: The aim of the paper is to examine the causal relationship between the
real property prices in biggest Polish cities within VAR model framework. Both offer
and transactional prices are used. Existing stock market, as well as primary market
are analysed. The data are quarterly and taken from 17 biggest Polish cities. The
analysed period is 2006-2015. Both VAR and VECM approaches were applied. Their
limitations and possible predictions were discussed. A significant interaction
between various regional real estate markets in Poland has been observed.
However, the leading role of the capital city could not be confirmed by the
methodology used.
Keywords: causality, property prices, Poland
JEL codes: R30
Introduction
The real property prices in Poland have significantly increased in past few years.
This situation is not just a Polish characteristic, but similar increases have been
observed in other economies. Some researchers suggest that a house price bubble
has occurred; in other words, that the situation cannot be explained on the basis
of fundamental factors (Żelazowski, 2011).
Developing theoretical models for the real property market is a challenge and the
same holds for the Polish market. The most important problem is the lack of a
suitably long time series. Only recently, Narodowy Bank Polski (2015) has started
to publish the reliable time series of house prices in biggest Polish cities. Of course
this is also because the free market is relatively recent phenomena in Poland.
Certain researches suggest that the sudden house price increase (especially large
between 2006 and 2007) was caused by certain socio-cultural factors. For example,
the increased interest of consumers in moving to large cities, which are
characterised by low unemployment, etc. (Żelazowski 2007). Indeed, there is some
evidence that the difference in the standard of living between large cities and other
regions of the country is continuously rising. Therefore, the increase in real property
prices in cities is connected with what these cities offer to their inhabitants: easier
access to education, healthcare, better chances of finding a good job, etc.
Yet, there are also some suggestions that the core of the price increase starts in
selected, most dynamically expanding, cities and other regions just follow the trend
6
(Drachal, 2014). Bełej and Kulesza (2014) applied various methods (Chebyshev
distance, the damped harmonic oscillator model, etc.) and concluded that the
capital city initiates the changes.
Therefore, it is interesting to analyse the causality of real property prices in Poland
with a help of the vector autoregression model (VAR). It seems that such an
analysis has not yet been done. It can help to identify regions which drive the house
prices. In this research the analysis has been restricted to the linearity assumption.
The aim of the paper is to examine the causal relationship between the real
property prices in the biggest Polish cities within VAR and VECM model frameworks.
1 Literature Review
Holmes (2007) suggested that for the UK developed market there is no consistent
long-run equilibrium relationship between various regions. However, cointegrated
regions can be found (Ashworth and Parker, 1997). On the other hand, Drake
(1995) concluded that development of real property prices is different in various
regions of UK and the observed differences in price trends are statistically
significant.
Meen (1999) postulated the existence of the so-called “ripple effect” in UK. In other
words, the changes of prices in a certain region result in the changes in some other
regions. However, Cook (2005a) noticed that the theoretical foundations of such
conclusions can suffer from some significant statistical biases. Recently, Montagnoli
and Nagayasu (2015) found that the house prices in UK can be grouped into four
convergence clubs.
Zohrabyan et al. (2008) concluded that there is a significant cointegration between
various regional property prices in the case of the US market. The “ripple effect”
was also confirmed by Lean and Smyth (2012) on a bit more exotic, Malaysian,
house market. Kyriazakou and Panagiotidis (2014) found that long-run causality in
UK is mainly linear, but the short-run one is non-linear. They also found that the
effect of the biggest town (London) on the other cities is the most important.
Holmes et al. (2011) found that that the speed of adjustment towards long-run
equilibrium is inversely related with a distance. Similar conclusions were found by
Holmes et al. (2017) for the Paris housing market. Bełej and Kulesza (2013) and
Bełej (2013) used bifurcation theory to model how unexpected changes on real
property market, even of small parameters, can result in large, structural changes.
The arguments for the causal relationship between house prices and credit policies
of banks are also important. Indeed, macroeconomic factors vary significantly
through regions. The causality tests of macroeconomic determinants and house
prices were reported, for example, by Jadevicius (2016) for the Lithuanian housing
market. However, the credit policies of banks are rather uniform. Of course, the
relative value of the property to wages, credit risk, unemployment rate, etc. vary
through regions. Still, the monetary policy, law regulations are quite uniform.
Therefore, certain changes can gradually spread over all regions. It should be
7
noticed that such interactions can be significant also at the multinational level
(Horvatova and Kelemenova, 2013). The discussion of Printzi and Panagiotidis
(2015) is also interesting in this context, as well as that of Nikolic (2015).
Lechowicz (2012) studied the impact of banking supervision and central bank
actions in UK on the real estate market. These institutions occurred to have a very
significant effect on the quantity of new housing space, investments, availability of
credit, cost of credit, wealth effect, etc. Wealth effect and the impact of the
liberalization of mortgage market on real property prices in UK were also thoroughly
studied by Muellbauer and Murphy (2012).
One can also consider the relationship between the domestic financial market and
real estate market (Okunev et al., 2000). Alexander and Barrow (1994) found a
significant impact of real property prices in selected regions on the prices in other
regions. They focused on the UK market and found that, especially, migrations play
an important role in determining the causal directions (Petrisor, 2012; Strelecek et
al., 2010).
Holmes and Grimes (2008) found that in the long term (i.e., between 1973 and
2006) house prices follow the same stochastic trend in various regions. The biggest
agglomeration (i.e., London) determines the prices in all other regions. The
smallest impact of London region is on the regions geographically far away from
London. However, they were very careful that the methodology used and the choice
of statistical tests heavily influenced the outcomes. Holly et al. (2011) confirmed
these conclusions. Moreover, they suggested that even the prices in US significantly
affect UK prices.
Similarly, Cook (2005b) observed that modelling with a certain asymmetric reaction
can significantly affect the conclusions. Indeed, manipulating this reaction can lead
to opposite outcomes. Meen (2002) also found important similarities between UK
and US real property markets. In the case of long-run relationship this was also
observed by Holly et al. (2010).
Yang et al. (2018) investigated the spillover in house prices in China. Their research
was based on a high-dimensional generalized VAR method and covered the period
between 2005 and 2015. Also, the biggest and middle size cities were considered.
The spillover effect was confirmed to exist.
2 Methodology and Data
The causality was simply checked with the help of VAR model (Sims, 1980). This
has several advantages, including flexibility and possible use of ordinary least
squares for all equations separately. There is also no division into endogenous and
exogenous variables. On the other hand, VAR model is considered a-theoretical.
There are problems with lag length selection. Moreover, for statistical test all
components should be stationary. However, one can just examine the relationship
8
between variables. Possible differencing (in order to achieve stationarity) can erase
the long-run information (Adkins, 2013; Brooks, 2008; Hill et al., 2011).
Formally, VAR model (Vector Auto-Regression) can be described in the following
way:
𝑦 = 𝑐 + 𝐴 𝑦 + ⋯ + 𝐴 𝑦 + 𝜀 (1)
where 𝑦 represents the vector of variables. In the above (vector) equation there
are k lags for each variable; 𝐴 denotes the matrix of coefficients; 𝜀 stands for the
error terms (it is a vector). Each error term should have zero mean. 𝜀 𝜀 should be
a positive semi-definite matrix and for every k>0 it should be 𝐸(𝜀 𝜀 ) = 0 , i.e.,
errors should not be autocorrelated (Lutkepohl, 2005).
The VAR model is applicable when all variables are stationary. Then each of the
single equations (constituting the vector notation used for the sake of clarity) can
be estimated by the standard Ordinary Least Squares (OLS) method. However, if
the variables are not stationary, then: if they are not cointegrated, then VAR might
be applied to their differences – but then the differences have to be stationary.
However, if the variables are cointegrated, then the error correction term has to be
included in VAR equation. Such models are called VECM (Vector Error Correction
Model).
The data were taken from the database of Narodowy Bank Polski (2015). Quarterly
data were used. The analysed the period starting in the 3rd quarter of 2006 and
ending in the 2nd quarter of 2015, resulting in 36 observations for each city. Both
offer and transaction prices were analysed, as well as the primary (bought from
and sold for the first time by a developer) and the existing stock markets (second
and next transactions). The database consists of real estate prices in 17 biggest
Polish cities, i.e., Białystok, Bydgoszcz, Gdańsk, Gdynia, Katowice, Kielce, Kraków,
Lublin, Łódź, Olsztyn, Opole, Poznań, Rzeszów, Szczecin, Warszawa, Wrocław, and
Zielona Góra.
Indeed, the selection of a suitable set of prices from the above options is an
interesting problem. Łaszek and Widłak (2008) and Łaszek and Olszewski (2014)
stressed that real property is not a homogenic product. Moreover, the market is
not liquid enough and assets cannot be divided enough in comparison to other
markets. The transactional prices can be artificially lowered because of the tax
optimization, etc. All computations were done in gretl software. If not stated
otherwise, the p-value in statistical tests is assumed to be 5%.
3 Results
The analysis started from a VAR estimation. The lag length was taken to be just 1.
Indeed, for example, Akaike information criterion should be used, but the
considered database consists of 36 observations only and taking more lags is
impossible due to the numerical restrictions.
9
The lack of long enough time series for Polish real estate market is a serious
problem which cannot be currently overcome. A priori it is assumed that there is
no long-run relationship between the variables. Therefore, VAR models were
estimated, but for logarithms of prices. The stationarity was checked with ADF test
with 9 lags and a constant.
The expression l_X denotes the logarithm of prices from town X. l_X_1 denotes the
first lag of logarithm of prices from town X. P-values in Appendices 1–4 refer to the
coefficients of the standard VAR model, i.e., coefficients a1,1 , … , a17,17 from the
below system of equations:
𝑙_𝐵𝑖𝑎ł𝑦𝑠𝑡𝑜𝑘 = 𝑐𝑜𝑛𝑠𝑡 + 𝑎 , 𝑙_𝐵𝑖𝑎ł𝑦𝑠𝑡𝑜𝑘_1 + ⋯ + 𝑎 , 𝑙_𝑍𝑖𝑒𝑙𝑜𝑛𝑎𝐺𝑜𝑟𝑎_1 (2)
...
𝑙_𝑍𝑖𝑒𝑙𝑜𝑛𝑎𝐺𝑜𝑟𝑎 = 𝑐𝑜𝑛𝑠𝑡 + 𝑎 , 𝑙_𝐵𝑖𝑎ł𝑦𝑠𝑡𝑜𝑘_1 + ⋯ + 𝑎 , 𝑙_𝑍𝑖𝑒𝑙𝑜𝑛𝑎𝐺𝑜𝑟𝑎_1 (3)
In Table 2, symbol d_l_X denotes the first difference of the logarithm of prices from
town X. P-values from Table 2 refer to coefficients a1 , … , a17 from the below system
of equations (the standard VECM model):
𝑑_𝑙_𝐵𝑖𝑎ł𝑦𝑠𝑡𝑜𝑘 = 𝑐𝑜𝑛𝑠𝑡 + 𝑎 𝐸𝑟𝑟𝑜𝑟𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 (4)
…
𝑑_𝑙_𝑍𝑖𝑒𝑙𝑜𝑛𝑎𝐺𝑜𝑟𝑎 = 𝑐𝑜𝑛𝑠𝑡 + 𝑎 𝐸𝑟𝑟𝑜𝑟𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 (5)
In the case of primary market transaction prices, all time-series of log of prices
were stationary (ADF test) at 5% significance level, except Białystok (p-value
0.3692), Kraków (p-value 0.8987), Lublin (p-value 0.204), Olsztyn (p-value
0.6772), Opole (p-value 0.7357), Rzeszów (p-value 0.9979), Wrocław (p-value
0.1955), and Zielona Góra (p-value 0.5318).
Appendix 1 presents the results of estimation of VAR model for primary market and
transaction prices. It should be noticed that only one lag was taken for each
variable. Therefore, using F-test (for joint significance of all lags) is the same as
performing t-test (for this one lag). Thus, the performed procedure is just the
standard Granger causality testing.
In the case of primary market offer prices, all time-series of log of prices were
stationary at 5% significance level, except: Białystok (p-value 0.3005), Gdańsk (pvalue
0.06127), Kraków (p-value 0.2582), Łódź (p-value 0.5877), Opole (p-value
0.05719), Szczecin (p-value 0.2756), Wrocław (p-value 0.2787), and Zielona Góra
(p-value 0.3885). This is quite similar as in the case of primary market transaction
prices.
10
Appendix 2 includes the results of estimation of VAR model for primary market and
offer prices.
In the case of existing stock market transaction prices, all time-series of log of
prices were stationary at 5% significance level, except Gdynia (p-value 0.5883),
Kraków (p-value 0.8715), Poznań (p-value 0.6716), Warszawa (p-value 0.7483),
and Wrocław (p-value 0.1824). This is much better than in the case of primary
market prices.
Appendix 3 presents the results of estimation of VAR model for existing stock
market and transaction prices. In the case of the existing stock market offer prices,
all time-series of log of prices were stationary at 5% significance level, except:
Katowice (p-value 0.1482), Kielce (p-value 0.8508), Olsztyn (p-value 0.9317),
Rzeszów (p-value 0.3949), Warszawa (p-value 0.7376), and Wrocław (p-value
0.1079). This is similar as in the case of the existing stock market transaction
prices.
Appendix 4 shows the results of estimation of VAR model for the existing stock
market and offer prices. Now, it can be seen that for short-run it is not the capital
city (Warszawa), which influences the highest number of other cities (Table 1).
Indeed, the most influencing city is Wrocław (which is also quite big) and
surprisingly, also Olsztyn (a rather small town). Yet, this can be also the result of
a high competition even on smaller regional markets (Kuryj-Wysocka and
Wiśniewski, 2013). Warszawa (the capital city) is still one of the most influencing
cities, but there are also some quite small ones like Kielce or Bydgoszcz whose
influence is important. For example, a big city – Kraków – is not as influential as
many other cities, for example, Rzeszów (a smaller town).
These results are quite surprising. However, they must be carefully interpreted.
The application of VAR assumes stationarity (which was found to be violated in
some cases) and lack of cointegration of variables (see, for example, the paper by
Drachal (2015)). The lack of cointegration was assumed a priori without any tests
herein. In this sense the paper of Kyriazakou and Panagiotidis (2014) was followed.
Moreover, as it was indicated, there are problems with stationarity. More on
stationarity and cointegration analysis for Polish property market can be found in
Drachal (2015).
Therefore, the Engle-Granger test of cointegration was performed (4 lags were
assumed). There is evidence for the cointegrating relationship if simultaneously the
unit-root hypothesis is not rejected for the individual variables, and the unit-root
hypothesis is rejected for the residuals from the cointegrating regression (Adkins,
2013; Fuller, 1976). At 5% significance level, in the case of the existing stock
market and offer prices, the first assumption was not met just for Kraków and
Opole, but the second one was met. Therefore, there is evidence of cointegration
for the existing stock market and offer prices.
At 5% significance level, in the case of the existing stock market and transaction
prices, the first assumption was not met just for Kraków and Zielona Góra, but also
11
the second one was not met. Therefore, there is no evidence of cointegration for
the existing stock market and transaction prices.
At 5% significance level, in the case of the primary market and offer prices, the
first assumption was not met for Białystok, Gdynia, Lublin, Poznań, Szczecin, and
Zielona Góra. However, the second one was met. Therefore, there is quite a weak
evidence of cointegration for the primary market and offer prices.
At 5% significance level, in the case of the primary market and transaction prices,
the first assumption was not met for Bydgoszcz, Gdynia, Kielce, Lublin, Olsztyn,
and Zielona Góra. However, the second one was met. Therefore, there is a weak
evidence of cointegration for the primary market and transaction prices.
These results suggest that for the existing stock market and offer prices, the
primary market and offer prices and the primary market and transaction prices,
VECM model should be estimated instead of VAR model.
Table 1 Number of other cities influenced by certain variables (VAR)
transaction
prices and
primary
market
offer prices
and primary
market
transaction
prices and
existing stock
market
offer prices
and existing
stock market
l_Bialystok_1 2 2 0 4
l_Bydgoszcz_1 5 5 5 5
l_Gdansk_1 4 2 2 2
l_Gdynia_1 4 3 6 2
l_Katowice_1 3 1 4 3
l_Kielce_1 0 7 5 6
l_Krakow_1 2 6 2 3
l_Lublin_1 2 5 5 2
l_Lodz_1 5 5 2 2
l_Olsztyn_1 6 5 4 4
l_Opole_1 3 3 1 1
l_Poznan_1 2 4 1 5
l_Rzeszow_1 1 8 4 5
l_Szczecin_1 3 9 2 2
l_Warszawa_1 6 5 3 2
l_Wroclaw_1 6 8 5 2
l_ZielonaGora_1 3 3 2 5
Source: Own calculations in gretl
Table 2 indicates that on the existing stock market and offer prices many cities
respond to disequilibrium between the selected region and other regions. On the
other hand, on the primary market and offer prices only 5 cities have such a
property. This can be, for example, the result of independent price policies of
12
developers in different regions. However, much more regions have such a property,
if transaction prices are considered. The results suggest that there is much
interaction on the regional level of real estate markets.
Table 2 P-values for error correction term (VECM)
existing stock
market and offer
prices
primary market
and offer prices
primary market
and transaction
prices
d_l_Bialystok 0.0008 0.0011 0.0000
d_l_Bydgoszcz 0.4226 0.4254 0.0000
d_l_Gdansk 0.0000 0.8960 0.0038
d_l_Gdynia 0.0273 0.1657 0.0002
d_l_Katowice 0.2877 0.7411 0.1228
d_l_Kielce 0.0002 0.2185 0.7596
d_l_Krakow 0.3840 0.0070 0.0038
d_l_Lublin 0.0003 0.0006 0.5966
d_l_Lodz 0.0006 0.5883 0.0001
d_l_Olsztyn 0.0000 0.0131 0.0033
d_l_Opole 0.0000 0.8754 0.9571
d_l_Poznan 0.0016 0.0495 0.0061
d_l_Rzeszow 0.0000 0.2400 0.2075
d_l_Szczecin 0.0003 0.8362 0.0000
d_l_Warszawa 0.0000 0.3095 0.1301
d_l_Wroclaw 0.0014 0.5872 0.6803
d_l_ZielonaGora 0.0280 0.3396 0.0005
Note: Statistically significant relationships are in bold. 10% p-value is assumed.
Source: Own calculations in gretl
The analysis suggested that there is a significant interaction between regional real
estate markets. However, it was hard to estimate the direct causal relationship.
First of all, certain problems with stationarity occurred, which indicate that VAR
model assumptions are violated in some cases. Secondly, the analysed time series
are very short. Unfortunately, there is a lack of more suitable data currently. These
drawbacks can result in significant biases in the presented results.
Conclusions
The motivation for the research reported in this paper was to examine the causal
relationship between the real property prices in biggest Polish cities. This task was
quite hard as the available time-series are not long enough to perform all standard
analyses. However, the VAR framework was applied. Offer and transactional prices
were used. Additionally, both the existing stock market and primary market were
13
analysed. However, due to some uncertainty about cointegrating properties of the
time-series both VAR and VECM models were estimated.
A significant interaction between various regional real estate markets in Poland has
emerged. However, the leading role of the capital city (Warszawa) cannot be
confirmed by the used methodology. Yet, the chosen methodology could not be
used in a pure and consistent way. Certain important problems were found.
Moreover, the lack of long enough time series occurred to be a really hard problem
to overcome. In the case of the existing stock market, almost every big city
responds to the disequilibrium with other regional markets. However, on the
primary market there are more cities which do not respond than the ones which do
so. Because of the indicated suggestions and found difficulties, this research can
serve as a starting point for some future, more detailed, research.
For example, the researcher having access to more frequent data can perform more
meaningful analysis. If monthly data are used, the number of observations should
be enough for reasonably performed cointegration tests, etc.
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Appendices
Appendix 1 P-values for VAR model of primary market transaction prices
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
const 0.7767 0.0966 0.0035 0.9783 0.0911 0.1560 0.0374 0.3601 0.1453 0.6949 0.1183 0.4056 0.0091 0.1403 0.0010 0.0026 0.7779
(1) l_Bialystok_1 0.5936 0.2764 0.9972 0.8880 0.9732 0.4504 0.7287 0.6101 0.4306 0.5492 0.3139 0.1814 0.6478 0.0378 0.2957 0.0238 0.1552
(2) l_Bydgoszcz_1 0.2575 0.0995 0.9532 0.7087 0.1785 0.0173 0.0674 0.0598 0.9958 0.0056 0.4867 0.3762 0.1914 0.8381 0.2825 0.3319 0.3057
(3) l_Gdansk_1 0.5347 0.9479 0.9516 0.7785 0.0694 0.6507 0.0469 0.6826 0.4922 0.0199 0.3681 0.5960 0.2331 0.1572 0.2414 0.0115 0.7606
(4) l_Gdynia_1 0.2556 0.1882 0.0128 0.1798 0.8308 0.0930 0.5487 0.2426 0.3753 0.3635 0.8880 0.6202 0.8345 0.4737 0.6551 0.3797 0.3206
(5) l_Katowice_1 0.7555 0.0047 0.3476 0.8321 0.6345 0.9507 0.3926 0.1248 0.5616 0.0333 0.8956 0.6866 0.8589 0.4395 0.0956 0.0794 0.5700
(6) l_Kielce_1 0.3423 0.4990 0.6366 0.2928 0.5354 0.4332 0.3503 0.9166 0.9013 0.4759 0.1918 0.2196 0.1792 0.4623 0.6277 0.4085 0.1129
(7) l_Krakow_1 0.2514 0.4545 0.1302 0.0539 0.4047 0.2453 0.0005 0.6239 0.1322 0.2050 0.8951 0.7710 0.1374 0.6060 0.7125 0.6191 0.6461
(8) l_Lublin_1 0.2626 0.3342 0.2924 0.6438 0.6767 0.3790 0.0695 0.9717 0.4475 0.7840 0.0791 0.2787 0.4657 0.2538 0.8992 0.9187 0.1231
(9) l_Lodz_1 0.5116 0.0250 0.0432 0.8034 0.6759 0.0413 0.1373 0.7267 0.8629 0.0383 0.1588 0.3441 0.7401 0.2406 0.2072 0.0008 0.3302
(10) l_Olsztyn_1 0.9944 0.5243 0.8021 0.0947 0.0054 0.0228 0.2025 0.8321 0.8381 0.0053 0.0431 0.5420 0.7581 0.7883 0.7189 0.0280 0.6642
(11) l_Opole_1 0.1038 0.6848 0.2337 0.0650 0.0107 0.7028 0.6004 0.5278 0.3457 0.6952 0.0558 0.2276 0.6251 0.4831 0.0042 0.7009 0.4632
(12) l_Poznan_1 0.7406 0.0058 0.0243 0.4436 0.1393 0.7371 0.3827 0.7497 0.6771 0.7537 0.3881 0.8409 0.9528 0.3433 0.3182 0.1711 0.7041
(13) l_Rzeszow_1 0.3223 0.5076 0.1333 0.4390 0.5617 0.2295 0.9691 0.7269 0.7894 0.0690 0.2700 0.8178 0.9784 0.9848 0.6437 0.4857 0.4542
(14) l_Szczecin_1 0.7908 0.0931 0.9267 0.8401 0.6996 0.3074 0.5236 0.8234 0.9363 0.2529 0.0855 0.1800 0.2315 0.9497 0.0037 0.0493 0.8256
(15) l_Warszawa_1 0.0722 0.0216 0.2778 0.3743 0.1631 0.6964 0.0668 0.6405 0.9280 0.0567 0.1331 0.0014 0.9775 0.9310 0.0018 0.9729 0.6730
(16) l_Wroclaw_1 0.0163 0.0003 0.2015 0.3619 0.0026 0.1926 0.4989 0.5192 0.0211 0.6232 0.7072 0.5250 0.1028 0.2123 0.5872 0.0279 0.0368
(17) l_ZielonaGora_1 0.8354 0.6458 0.2277 0.9820 0.0079 0.3110 0.7155 0.1248 0.9247 0.8822 0.3111 0.2943 0.0833 0.2928 0.0054 0.1689 0.7836
Note: Statistically significant relationships are in bold. 10% p-value is assumed.
Source: Own calculations in gretl
18
Appendix 2 P-values for VAR model of primary market offer prices
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
const 0.0598 0.0003 0.0399 0.0088 0.5583 0.4826 0.5376 0.0651 0.5945 0.1353 0.2249 0.0912 0.2283 0.1082 0.0011 0.0037 0.8693
(1) l_Bialystok_1 0.0738 0.1203 0.1402 0.2613 0.3484 0.1623 0.7176 0.1600 0.1454 0.7574 0.2427 0.2593 0.2657 0.7051 0.0120 0.3562 0.8844
(2) l_Bydgoszcz_1 0.1532 0.3837 0.7393 0.2493 0.8976 0.3520 0.0260 0.1999 0.0926 0.9908 0.0049 0.6777 0.7069 0.0381 0.6928 0.0951 0.1175
(3) l_Gdansk_1 0.1377 0.0205 0.1758 0.7811 0.1575 0.8791 0.2718 0.3519 0.6922 0.4583 0.5232 0.3541 0.2500 0.2023 0.1476 0.0044 0.7930
(4) l_Gdynia_1 0.5473 0.0894 0.7784 0.0755 0.9935 0.6342 0.8541 0.3914 0.5227 0.6558 0.1573 0.6409 0.5384 0.9702 0.0060 0.7488 0.4844
(5) l_Katowice_1 0.8249 0.7493 0.2324 0.2304 0.0946 0.6189 0.4697 0.2189 0.8529 0.6944 0.6705 0.5553 0.8112 0.5521 0.5523 0.1977 0.6863
(6) l_Kielce_1 0.2265 0.0497 0.3396 0.1392 0.2783 0.2362 0.0979 0.0234 0.0786 0.2636 0.4910 0.4731 0.3026 0.4168 0.0043 0.0333 0.0726
(7) l_Krakow_1 0.1878 0.0042 0.9875 0.1173 0.3772 0.9968 0.0008 0.0223 0.0684 0.0530 0.1175 0.6362 0.0207 0.9099 0.7685 0.3007 0.2635
(8) l_Lublin_1 0.0081 0.3263 0.1114 0.0856 0.7340 0.3506 0.1307 0.2685 0.1881 0.2385 0.3098 0.0221 0.9257 0.0489 0.0391 0.7784 0.5886
(9) l_Lodz_1 0.2356 0.0062 0.4898 0.0725 0.3078 0.4732 0.0651 0.5070 0.1488 0.9150 0.3323 0.3970 0.7157 0.0854 0.0149 0.4432 0.9559
(10) l_Olsztyn_1 0.0140 0.0389 0.2224 0.0102 0.8986 0.8235 0.0157 0.2295 0.1291 0.8732 0.7797 0.1866 0.2323 0.2740 0.0037 0.3093 0.6577
(11) l_Opole_1 0.4662 0.8959 0.4624 0.4826 0.4068 0.8403 0.3287 0.0368 0.2588 0.4081 0.0734 0.4726 0.5172 0.3409 0.0398 0.7154 0.2036
(12) l_Poznan_1 0.1184 0.5845 0.4960 0.2808 0.6476 0.7976 0.2310 0.5464 0.0089 0.6322 0.9540 0.5678 0.2574 0.0286 0.9101 0.0208 0.0002
(13) l_Rzeszow_1 0.0039 0.0249 0.4582 0.1824 0.4617 0.0687 0.0023 0.2194 0.1980 0.1522 0.0976 0.0039 0.0087 0.0081 0.6720 0.3520 0.7537
(14) l_Szczecin_1 0.0002 0.0105 0.2359 0.0076 0.0976 0.7670 0.0346 0.0028 0.3407 0.0269 0.1006 0.0765 0.6930 0.0115 0.1277 0.1401 0.2378
(15) l_Warszawa_1 0.0198 0.0597 0.1786 0.2402 0.8974 0.4908 0.1744 0.1584 0.3705 0.2379 0.9612 0.0876 0.2977 0.0138 0.0256 0.3561 0.9877
(16) l_Wroclaw_1 0.0140 0.0004 0.3098 0.0080 0.5604 0.9594 0.0232 0.1113 0.4303 0.1551 0.5248 0.6505 0.0009 0.1318 0.0344 0.0086 0.0001
(17) l_ZielonaGora_1 0.6692 0.0032 0.4451 0.1146 0.8907 0.4566 0.1736 0.7540 0.3262 0.7156 0.0105 0.3257 0.5814 0.8158 0.0367 0.7542 0.1068
Note: Statistically significant relationships are in bold. 10% p-value is assumed.
Source: Own calculations in gretl
19
Appendix 3 P-values for VAR model of the existing stock market transaction prices
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
const 0.4412 0.9009 0.5604 0.5574 0.2380 0.0109 0.0233 0.2151 0.2378 0.0009 0.0052 0.2186 0.1607 0.0413 0.0108 0.2546 0.1011
(1) l_Bialystok_1 0.4049 0.1442 0.9234 0.3819 0.4009 0.7938 0.7621 0.4602 0.8885 0.3689 0.2864 0.6430 0.8238 0.7873 0.4747 0.5710 0.4317
(2) l_Bydgoszcz_1 0.6400 0.3556 0.0155 0.0790 0.0349 0.4643 0.3459 0.5026 0.9029 0.5616 0.4365 0.8830 0.3420 0.7560 0.0690 0.8175 0.0281
(3) l_Gdansk_1 0.7337 0.4015 0.9462 0.7340 0.2594 0.0553 0.9552 0.6417 0.7749 0.5785 0.2274 0.2447 0.5018 0.8920 0.0467 0.9871 0.5452
(4) l_Gdynia_1 0.0433 0.5869 0.0272 0.2356 0.9282 0.7390 0.1485 0.0136 0.0048 0.4741 0.1920 0.7491 0.0929 0.3514 0.6117 0.8500 0.0756
(5) l_Katowice_1 0.3224 0.8834 0.0930 0.0873 0.0049 0.1830 0.1169 0.2023 0.1695 0.4164 0.6339 0.5316 0.3084 0.3312 0.0311 0.5415 0.2166
(6) l_Kielce_1 0.9512 0.8162 0.0562 0.9170 0.4963 0.0627 0.1785 0.0816 0.3731 0.3073 0.0418 0.7688 0.3216 0.8419 0.4592 0.1610 0.0694
(7) l_Krakow_1 0.3575 0.9536 0.8059 0.4206 0.3405 0.0629 0.7793 0.6919 0.7528 0.3888 0.5399 0.6870 0.7313 0.8618 0.0411 0.7720 0.2020
(8) l_Lublin_1 0.1634 0.6895 0.3507 0.0959 0.2881 0.7718 0.2197 0.0305 0.3396 0.1055 0.0442 0.0567 0.8123 0.3409 0.0026 0.3431 0.4913
(9) l_Lodz_1 0.1829 0.4902 0.9831 0.6528 0.2853 0.1285 0.6050 0.9249 0.2801 0.1261 0.0866 0.1707 0.1846 0.9049 0.4956 0.6367 0.0022
(10) l_Olsztyn_1 0.2701 0.5332 0.4915 0.2847 0.0510 0.0008 0.1350 0.7325 0.2435 0.0092 0.6943 0.0664 0.5762 0.6954 0.2928 0.2203 0.4722
(11) l_Opole_1 0.9405 0.8677 0.7356 0.3754 0.5212 0.1547 0.6343 0.8978 0.9246 0.7786 0.7114 0.5116 0.8073 0.0334 0.3670 0.4311 0.5566
(12) l_Poznan_1 0.4958 0.5762 0.9420 0.6557 0.2549 0.3570 0.5893 0.5460 0.4669 0.7822 0.0271 0.5458 0.4770 0.1881 0.6604 0.5802 0.2868
(13) l_Rzeszow_1 0.2146 0.4277 0.1190 0.5811 0.0856 0.6265 0.1036 0.9376 0.0097 0.4891 0.0260 0.2933 0.0065 0.8799 0.2990 0.9184 0.8125
(14) l_Szczecin_1 0.2916 0.1849 0.5813 0.1745 0.0920 0.1696 0.7100 0.4563 0.2584 0.9724 0.9443 0.6419 0.5539 0.0372 0.9360 0.8178 0.4909
(15) l_Warszawa_1 0.7614 0.7649 0.1361 0.2196 0.0375 0.4660 0.6452 0.0711 0.5498 0.3330 0.0978 0.5102 0.2724 0.6571 0.1304 0.4738 0.5195
(16) l_Wroclaw_1 0.0301 0.7187 0.8246 0.8981 0.1141 0.6132 0.0615 0.0315 0.7471 0.0536 0.0352 0.8709 0.3917 0.5691 0.3522 0.2322 0.1188
(17) l_ZielonaGora_1 0.4499 0.8496 0.4932 0.5331 0.0203 0.2149 0.6380 0.2642 0.8581 0.5736 0.0707 0.2640 0.2166 0.6575 0.9798 0.6912 0.7066
Note: Statistically significant relationships are in bold. 10% p-value is assumed.
Source: Own calculations in gretl
20
Appendix 4 P-values for VAR model of the existing stock market offer prices
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
const 0.2471 0.4583 0.0935 0.0028 0.1277 0.7642 0.0489 0.1139 0.6974 0.0176 0.0303 0.2298 0.0001 0.0651 0.0063 0.2887 0.0140
(1) l_Bialystok_1 0.0507 0.0151 0.1058 0.5795 0.8001 0.1430 0.2714 0.0930 0.8669 0.2998 0.3218 0.0717 0.2216 0.7326 0.3544 0.8461 0.3106
(2) l_Bydgoszcz_1 0.1892 0.0705 0.6300 0.5549 0.0634 0.7520 0.3566 0.0145 0.7791 0.8696 0.0322 0.7508 0.6647 0.5553 0.6952 0.0589 0.9985
(3) l_Gdansk_1 0.5837 0.4790 0.2117 0.8088 0.5821 0.9476 0.0123 0.1155 0.9969 0.9599 0.1371 0.0764 0.8089 0.5119 0.6377 0.4756 0.2601
(4) l_Gdynia_1 0.9855 0.0182 0.9661 0.8320 0.5325 0.2379 0.1576 0.9717 0.7281 0.1687 0.4833 0.1088 0.1278 0.1313 0.4184 0.2304 0.0468
(5) l_Katowice_1 0.2568 0.0461 0.9840 0.4754 0.6884 0.8934 0.2146 0.0364 0.5889 0.1504 0.8358 0.0074 0.7213 0.5058 0.3499 0.1906 0.3232
(6) l_Kielce_1 0.0008 0.2854 0.0221 0.4388 0.6341 0.0501 0.1142 0.6083 0.9379 0.0150 0.3080 0.0081 0.4859 0.8270 0.0587 0.6847 0.5730
(7) l_Krakow_1 0.1265 0.2206 0.1742 0.1375 0.7739 0.3799 0.0018 0.2303 0.8739 0.4335 0.0208 0.1476 0.7277 0.0178 0.7853 0.5647 0.4381
(8) l_Lublin_1 0.3514 0.2127 0.9623 0.7234 0.9641 0.0245 0.7706 0.4766 0.2480 0.0252 0.4363 0.2893 0.5272 0.1007 0.5036 0.8217 0.4234
(9) l_Lodz_1 0.1768 0.9875 0.9051 0.0827 0.7132 0.1039 0.2549 0.2858 0.1438 0.5971 0.2200 0.0039 0.9408 0.8863 0.6390 0.4389 0.8270
(10) l_Olsztyn_1 0.4272 0.3917 0.6503 0.0999 0.3091 0.9238 0.4092 0.7468 0.6869 0.0203 0.1423 0.4699 0.6363 0.8166 0.6050 0.0326 0.0130
(11) l_Opole_1 0.3544 0.1412 0.3245 0.7640 0.2505 0.9516 0.2401 0.1517 0.8708 0.2102 0.8086 0.4516 0.8985 0.8648 0.0528 0.2171 0.9548
(12) l_Poznan_1 0.1007 0.0850 0.1019 0.0261 0.7470 0.6872 0.8153 0.0174 0.9774 0.8302 0.0175 0.0142 0.1516 0.1817 0.7370 0.5535 0.5225
(13) l_Rzeszow_1 0.2879 0.5212 0.1835 0.0957 0.0011 0.0500 0.1389 0.8630 0.5990 0.1154 0.0040 0.0049 0.0004 0.0657 0.0017 0.3695 0.0009
(14) l_Szczecin_1 0.8668 0.3115 0.7993 0.6954 0.2196 0.1449 0.9978 0.0709 0.6269 0.5892 0.4536 0.2310 0.5031 0.4986 0.0680 0.9797 0.6465
(15) l_Warszawa_1 0.2439 0.9254 0.9251 0.8957 0.1340 0.0026 0.4188 0.9824 0.2687 0.6100 0.1220 0.1560 0.7527 0.0234 0.4908 0.4278 0.6024
(16) l_Wroclaw_1 0.2363 0.3699 0.3372 0.7519 0.1624 0.1200 0.1250 0.7892 0.7094 0.0213 0.3443 0.7928 0.7129 0.1417 0.2774 0.0042 0.2902
(17) l_ZielonaGora_1 0.0650 0.0078 0.2786 0.0745 0.6631 0.1410 0.8450 0.3850 0.3282 0.1032 0.0393 0.8490 0.0183 0.1123 0.6106 0.2495 0.2424
Note: Statistically significant relationships are in bold. 10% p-value is assumed.
Source: Own calculations in gretl